LONDON—Rising crude prices are supercharging earnings at the world’s major oil firms, but investors may need more convincing that Big Oil is back.

Sharply climbing oil prices—and years of cost cutting when they were low—are rewarding some of the world’s largest oil producers with profits not seen since crude was trading around $100 a barrel. Despite that, investors remain wary. As the industry emerges from a long and painful few years of low prices, shareholders are pressing executives to keep spending in check and funnel free cash to shareholders.

Royal Dutch Shell PLC reported Thursday its highest quarterly profit since 2013, when prices were peaking just ahead of a steep downdraft to about $25 a barrel. Today, international crude is back comfortably above $70 a barrel, and oil companies have enjoyed three months of strong pricing for their crude.

The Anglo-Dutch oil giant said its first-quarter profit on a current cost-of-supplies basis—a number similar to the net income that U.S. oil companies report—rose 69% from a year earlier to $5.7 billion. The company delivered more than $5 billion in free cash flow—a newly important metric for investors who grew concerned about big oil companies’ ability to finance their generous dividends during recent years of lower oil prices.

Underscoring the still-skittish sentiment, though, Shell shares were down 2.5% in London morning trading after operating cash flow came in below analysts’ expectations.

Shell is the biggest oil company yet to report results for the quarter—a period when the industry will be under a microscope. After years of retrenchment, investors are expecting companies to deliver them billions of dollars in cash, buoyed by rising oil prices and stringent cost cuts.

Pressure remains on firms to keep spending constrained. Executives have signaled that despite the heady oil prices, they will keep costs in check and spin out cash to investors, instead of betting the gains on new expensive but risky oil-field investments.

“They just need to stick to their knitting,” said Rohan Murphy, energy analyst at Allianz Global Investors, a Shell investor. He said the industry’s leadership needs to “show that they’re not going to start spending willy-nilly again.”

France’s Total SA also reported first-quarter earnings Thursday, beating expectations for profit after stripping out one-off items. The company’s production rose to record levels.

But net profit slipped 7% compared with a year earlier, suffering from a tough comparison a year earlier, when it booked a big gain from an asset sale. Higher oil prices also acted as a double-edged sword for Total, adding to costs and crimping margins at its refining operations.

Shares in Norway’s Statoil ASA fell nearly 3% Wednesday after its profit numbers missed expectations. High crude prices boosted earnings and cash flow at the company, too, but results suffered from higher depreciation expenses in Norway and weaker earnings from the company’s trading and refining unit.

Exxon Mobil Corp. and Chevron Corp. are set to disclose their first-quarter results Friday. BP PLC reports next week. All three are expected to generate higher profits and lots of cash.

Total on Thursday raised its first-quarter interim dividend 3.2%, in line with plans announced in February. It has targeted increasing shareholder payouts 10% over the next three years.

Shell said it is on track to buy back at least $25 billion worth of shares by 2020, but gave no indication when the previously flagged program would begin. Some investors were hoping for more clarity on those plans.

Statoil has also held up the prospect of a buyback, but didn’t provide new details about timing this week.

“We still see emerging scope for buybacks but it would depend on the macro environment,” Statoil Chief Executive Eldar Saetre said in an interview. “We see a lot of volatility.”